The volume of a sphere is 48 m3 . What is the volume of a cylinder if its radius is the same as the sphere’s and its height is equal to the sphere’s diameter?(1 point)
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To find the volume of a cylinder, we need to know the formula for the volume of a cylinder.
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given that the radius of the cylinder is the same as the sphere's, and the height is equal to the sphere's diameter, we can substitute these values into the formula.
First, we need to find the radius and height of the sphere:
The volume of the sphere is given as 48 m^3.
The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
We can rearrange this formula to solve for the radius:
48 = (4/3)πr^3
Multiplying both sides by 3/4:
36 = πr^3
Dividing both sides by π:
r^3 = 36 / π
Taking the cube root of both sides to solve for r:
r = (36 / π)^(1/3)
Now that we have the radius of the sphere, we can find the height of the cylinder, which is equal to the diameter of the sphere:
d = 2r
Substituting the value of r:
d = 2 * (36 / π)^(1/3)
The height of the cylinder is the same as the diameter of the sphere:
h = 2 * (36 / π)^(1/3)
Now we can calculate the volume of the cylinder using the formula V = πr^2h:
V = π * (36 / π)^(2/3) * (2 * (36 / π)^(1/3))
Simplifying:
V = 2 * 36^(2/3) * (36 / π)^(1/3)
Since there are no given values for the radius or height, we cannot calculate the exact volume of the cylinder in cubic meters. We can only provide a general formula for the volume of the cylinder in terms of the given values.